House immigration negotiators have given themselves until the end of the week to hash out language on what kind of health benefits should be available to undocumented immigrants seeking U.S. citizenship, a crucial issue for the talks.

If they can’t resolve this issue, the four-year immigration negotiations could come to a crashing halt.

Top Democrats said late Tuesday they do not think Republicans will walk away from the talks.

It was only less than a week ago that the bipartisan House group announced it had reached a tentative agreement on a proposal “in principle” to be introduced in June.

The provision, in essence, said immigrants seeking citizenship must provide their own health care — and if any government entity provides them with services, they would be ineligible for permanent citizenship. The language was aimed at assuaging Republican concerns that the immigration bill would plunge the nation further into debt.

But as word spread, top Democrats — including House Minority Leader Nancy Pelosi (D-Calif.) and Minority Whip Steny Hoyer (D-Md.) — began to grow uncomfortable with the language their party drafted to prevent undocumented immigrants from taking advantage of government-subsidized health care.

Top Democrats are concerned that in emergency situations, for example, undocumented immigrants would be forced to undergo procedures that could bankrupt them, and eventually lead to deportation.

“They wrote it,” said Rep. John Carter (R-Texas), a member of the bipartisan group, referring to the initial language.

The situation is so tenuous that there have been constant Democratic leadership meetings with immigration negotiators — two in the past 24 hours. Just hours after a Tuesday afternoon gathering, Pelosi called a leadership meeting for Wednesday at 10 a.m.

At a meeting late Monday, Pelosi twice got into a “lively discussion” with Rep. Luis Gutierrez (D-Ill.) — a member of the immigration group — claiming that they went beyond their purview of negotiating an immigration compromise.

The situation illustrates how remote a bipartisan House agreement is, although it seemed close a few days ago.

House Republican and Democratic immigration negotiators are spending this week tripping over each other, trying to explain how the bipartisan accord they thought they had last week is close to falling apart at the seams.

It’s a big step back for the prospects of immigration reform. Without a bipartisan House bill, Speaker John Boehner’s chamber won’t have as much buy-in to the process.

Behind the scenes, the situation is getting messy.

Democrats and Republicans in the immigration group are increasingly frustrated with Rep. Xavier Becerra (D-Calif.), who was noncommital to the health care language before it was released, while most of the group agreed, according to several sources involved in the negotiation.

So now, as the agreements come undone, a secret legislative process is unraveling in public view. The deal that canceled staff trips and kept aides busy during recesses is crumbling.

And as their Senate counterparts wrap up their bipartisan compromise in committee, Democrats and Republicans find themselves fighting on familiar ground — health care.

Indeed, Democratic leadership has serious problems with the language agreed to in the talks. Senior Democratic aides have griped that the group went far beyond immigration policy, and is now negotiating the Affordable Care Act behind closed doors.

And now, after giving the rank and file free rein to negotiate a sweeping immigration proposal, Democratic leadership is trying to figure out how — and if — they should proceed.

The stakes are high for both parties.

On Tuesday, Pelosi gathered top Democrats involved in the negotiations for a strategy session: Hoyer, Becerra, Reps. Zoe Lofgren of California, Gutierrez, John Yarmuth of Kentucky; and longtime Pelosi allies California Reps. Henry Waxman and George Miller, to strategize.

“We are watching this very closely so they don’t inadvertently do something they shouldn’t,” a senior Democrat involved in the talks told POLITICO.

And Republicans, who have spent years trying to defang the health care law, cannot support a bill that could add more patients to government-subsidized health care. Democrats think they can’t even pass anything out of the GOP-controlled House without Democratic support.

After he emerged from Pelosi’s office, Miller said “of course” there is health care language that Democrats can agree on.

“I don’t do their negotiations,” Miller said, when pressed about what that language would look like. Asked about his role in the talks, Miller said he was a “a sage” to the talks.

On Tuesday, Hoyer said leadership was “absolutely not” pulling the plug on the House negotiations.

“They’re still working and trying to get to a final agreement,” Hoyer said. “Obviously, the details — to some degree — have to be worked out. And I don’t think the leadership is going to take any position until that’s done.”

There appear to be parallel efforts to save the bill. Lofgren and Gutierrez, who both declined to speak to reporters Tuesday evening, were huddled with Rep. Paul Ryan (R-Wis.) on the House floor Tuesday afternoon. The full, bipartisan group met Tuesday night, where they discussed the end-of-week deadline, according to sources familiar with the talks.

Becerra, for his part, says the negotiations are going swimmingly.

“We’re having some good conversations about how to try to move this forward,” he said.

When told that Republicans are saying the negotiations are nearing a point of no return, Becerra said, “We keep having conversations with them, and we’re having our bipartisan meetings, so we feel good about the opportunities to close this up and get this done.”